Let \(\tilde{\Lambda }:=(S^{-1}_{\Lambda }W_j, \Lambda _j \pi _{W_j}S_{\Lambda }^{-1}, v_j)\) . Then, \(\tilde{\Lambda }\)  is called the (canonical) dual g-fusion frame of \(\Lambda \) . Hence, for each \(f\in H\) , we get (see [1]})
\(f=\sum _{j\in J}v_j^2\pi _{W_j}\Lambda ^*_j\tilde{\Lambda _j}\pi _{\tilde{W_j}}f=\sum _{j\in J}v_j^2\pi _{\tilde{W_j}}\tilde{\Lambda _j}^*\Lambda _j\pi _{W_j}f,\) 
